jtfifcellanea Curio fa. 3 I 



the difference of the Latitudes,divided by thrice 

 the Verfed-fine of the fum of the Co-latitudes, 

 &c. which is the utmoft Compendium 1 can think 

 of for this purpofe, and the fame feries will 

 become, 



•into i 



aS iV" 5^ nJ n 1 9/^- 



Hereby we are enabled to eflimate the de- 

 fault of the method of making the Meridian 

 line, by the continued addition of the Secants 

 of aequidifferent Arches, which as the difference 

 of thofe Arehes are frnaller, does ftill nearer 

 and nearer approach the Truth. If we affume, 

 as Mr. Wright did, the Arch of one minute to 

 be Unity, and one minute to be the common 

 difference of a rank of Arches : It will be in all 

 cafes, as the Arch of one Minute, to its Chord 

 : : So the Secant of the middle Latitude, to 

 the firft ftep of our feries. This by reafon of 

 the near equality between a and i which are 

 to one another in the ratio of Unity to i— o, 

 00000000352566457713, &c. will not differ 

 from the Secant /but in the ninth Figure ; be- 

 ing lefs than it in that proportion. The next 

 2. s * 



ftep being -y— r w ^ ^ e equal to the Cube 



of the Secant of the middle Latitude multiply 



ed into 0,00000000705132908715 j 



which therefore unlefs the Secant exceed ten 

 times Radius, can never amount to 1 in the fifth 

 place. Thefe two fteps fuffice to make the 

 Meridian Line, or Logarithm Tangent to far 

 more places than any Tables of Natural Se- 



cafes ? 



